High Statistics Analysis using Anisotropic Clover Lattices: (IV) Volume Dependence of Light Hadron Masses

TL;DR

This study investigates how the masses of light hadrons vary with lattice volume in Lattice QCD, comparing results with chiral perturbation theory predictions to improve understanding of finite-volume effects.

Contribution

It provides a detailed analysis of volume dependence of baryon and meson masses using anisotropic clover lattices and compares findings with chiral perturbation theory predictions.

Findings

Volume dependence matches three-flavor chiral perturbation theory reasonably well.

Finite-volume effects are smaller at physical pion mass (~140 MeV) than at 390 MeV.

Delta-N-pi axial coupling constant is extracted from nucleon mass volume dependence.

Abstract

The volume dependence of the octet baryon masses and relations among them are explored with Lattice QCD. Calculations are performed with n_f=2+1 clover fermion discretization in four lattice volumes, with spatial extent L ~ 2.0, 2.5, 3.0 and 3.9 fm, with an anisotropic lattice spacing of b_s ~ 0.123 fm in the spatial direction, and b_t = b_s/3.5 in the time direction, and at a pion mass of m_pi ~ 390 MeV. The typical precision of the ground-state baryon mass determination is ~0.2%, enabling a precise exploration of the volume dependence of the masses, the Gell-Mann--Okubo mass relation, and of other mass combinations. A comparison of the volume dependence with the predictions of heavy baryon chiral perturbation theory is performed in both the SU(2)_L X SU(2)_R and SU(3)_L X SU(3)_R expansions. Predictions of the three-flavor expansion for the hadron masses are found to describe the observed volume dependences reasonably well. Further, the Delta-N-pi axial coupling constant is extracted from the volume dependence of the nucleon mass in the two-flavor expansion, with only small modifications in the three-flavor expansion from the inclusion of kaons and etas. At a given value of m_pi L, the finite-volume contributions to the nucleon mass are predicted to be significantly smaller at m_pi ~ 140 MeV than at m_pi ~ 390 MeV due to a coefficient that scales as ~ m_pi^3. This is relevant for the design of future ensembles of lattice gauge-field configurations. Finally, the volume dependence of the pion and kaon masses are analyzed with two-flavor and three-flavor chiral perturbation theory.